The probability that a sample of size n = 158 is randomly selected with a mean greater than 242.4 is 0.751.
How to calculate the probabilityz = (x - μ) / (σ/√n)
where x is the sample mean.
Substituting the values, we get:
z = (242.4 - 246) / (89.7/√158) ≈ -0.670
We want to find the probability of obtaining a sample mean greater than 242.4, which is equivalent to finding the probability of obtaining a standardized sample mean greater than z = -0.670. We can use a standard normal distribution table or calculator to find this probability.
P(z > -0.670) ≈ 0.751
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Find the missing variables. Write answer as
number. For example: If answer is 31° type
31
X=
□2°
xº
36°
y=
Z=
yᵒ
75%
78°
The values of missing variables are given by:
x = 51°, y = 105°, z = 90°.
We know that the sum of external and internal angles is 180°.
So from the given figure we can see that y° is the external angle and the corresponding internal angle is 75°.
So, 75° + y° = 180°
y° = 180° - 75° = 105°
And also external angle is right angle that is 90° and the corresponding internal angle is z°.
So, z° + 90° = 180°
z° = 180° - 90° = 90°
This is a pentagon and the sum of all internal angles = (5 - 2)180° = 3*180° = 540°
According to the given figure the sum of all internal angles of the pentagon is = (180° - 36°) + z° + (180° - x°) + (180° - 78°) + 75° = 144° + 90° + 180° - x + 102° + 75° = 591° - x.
So, 591° - x = 540°
x = 591° - 540° = 51°
Hence the value of missing variables are: x = 51°, y = 105°, z = 90°.
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Calculate standard deviation for the following by direct and shortcut method.assume mean as 32
Serial no.of workers
1
2
3
The standard deviation for the given distribution is 8.739 using either the direct method or the shortcut method.
How to find the standard deviation?Standard deviation is defined as a measure of how spread out numbers are. It is also referred to as the square root of the Variance, and then the Variance is the average of the squared differences from the Mean.
To calculate the standard deviation for the given distribution, we will utilize either the direct method or the shortcut method.
Direct method:
Calculate the mean wage (F) for the distribution:
Mean = (20 + 22 + 27 + 30 + 31 + 32 + 35 + 45 + 40 + 48)/10
Mean = 34
Calculate the differences between each wage and the mean wage:
20 - 34 = -14
22 - 34 = -12
27 - 34 = -7
30 - 34 = -4
31 - 34 = -3
32 - 34 = -2
35 - 34 = 1
45 - 34 = 11
40 - 34 = 6
48 - 34 = 14
Square each of the differences:
(-14)² = 196
(-12)² = 144
(-7)² = 49
(-4)² = 16
(-3)² = 9
(-2)² = 4
1² = 1
11² = 121
6² = 36
14² = 196
Add up the squared differences: 196 + 144 + 49 + 16 + 9 + 4 + 1 + 121 + 36 + 196 = 756
Divide the sum of the squared differences by the number of workers: 756/10 = 75.6
Take the square root of the result to get the standard deviation:
√75.6 = 8.739
Shortcut method:
The mean wage (F) for the distribution:
(20 + 22 + 27 + 30 + 31 + 32 + 35 + 45 + 40 + 48)/10 = 34
The sum of the squares of the differences between each wage and the mean wage:
(20 - 34)² + (22 - 34)² + (27 - 34)² + (30 - 34)² + (31 - 34)² + (32 - 34)² + (35 - 34)² + (45 - 34)² + (40 - 34)² + (48 - 34)² = 756
Divide the sum by the number of workers: 756/10 = 75.6
Take the square root of the result to get the standard deviation:
Standard deviation = √75.6 = 8.739
Therefore,
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Complete question is:
Calculate standard deviation for the following
distribution by direct and shortcut method.
Assume mean as 32.
Serial No. of Workers
1
2
3
4
5
6
7
8
9
10
Wage (F)
20
22
27
30
31
32
35
45
40
48
What is the least common dominator of 4/13 and 4/5?
Answer:
52 is the least common dominator
Answer:
52/65
Step-by-step explanation:
The same fraction we can express in many different forms. If the numerator and denominator ratio is the same, the fractions represent the same rational number.
The least common denominator of a set of fractions is the least number that is a multiple of all the denominators: their least common multiple
The method of calculating the LCD is the same as the calculation least common multiple of fractions denominators.
The simple method for common computing denominators (not least at all) is to multiply all denominators.
Exercise 17.5 Calculate the curved surface a cone whose height is 8 cm and base radius 5cm
The curved surface area of the cone is 148 cm².
Given that we need to find the curved surface area of the cone with height of 8 cm and radius of 5 cm,
The curved surface area gives the area of the face of an object.
The CSA of a cone = π × radius × slant height.
Slant height = √r²+h²
= √64+25
= 9.43 cm.
Now the csa = 3.14 × 5 × 9.43
= 148
Hence the curved surface area of the cone is 148 cm².
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There are 16 green balls and 4 white balls in a bag. Four balls are drawn randomly from the bag. Let X be the number of white balls drawn.
(a) Find the expectation and variance of X.
Answer:
the variance of X is 0.126.
Step-by-step explanation:
The number of white balls drawn X follows a hypergeometric distribution with N = 20 (total number of balls), K = 4 (number of balls drawn), and n = 4 (number of white balls). The probability mass function (pmf) of X is given by:
P(X = k) = (nCk)(N-nCk) / (NCk)
where C denotes the combination function.
(a) Expectation of X:
E(X) = np = nK/N = (4/20) * 4 = 0.8
Therefore, the expected number of white balls drawn is 0.8.
(b) Variance of X:
Var(X) = np(1-p)[(N-K)/(N-1)] = nK(N-K)(N-n)/(N^2(N-1)) = (4/20) * 4 * (20-4) * 16 / (20^2 * 19) = 0.126
Therefore, the variance of X is 0.126.
Answer:
The expected number of white balls drawn is 0.4 and the variance of X is 0.24.
Step-by-step explanation:
Ruth has a cylindrical cup that is filled with water. The cup has a diameter of 2 inches and a height of 6 inches. Select the containers that could hold all of the water in Ruth's cup
Since the containers were not given in the question, In a case whereby Ruth has a cylindrical cup that is filled with water where the cup has a diameter of 2 inches and a height of 6 inches, the volume of cylinder cup is 18.85inch^3.
How can the volume be calculated?Note that ; the container were not given in the question, so we will just need to calculate the volume of the cylindrical cup to know how much water it can hold .
The volume of a cylinder can be caluculated using te exppresion π r² h
Then from the question the diameter = 2 inches radius = 2/2 = 1 inches
height =6 inches
π r² h
=π * 1^2 * 6
=18.85inch^3
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helppp me its need to be done quick
Answer:
100
Step-by-step explanation:
The number has the same digit in its hundreds place and its hundredths place. The digit in the hundreds place is 100 times greater than the digit in the hundredths place (https://ccssmathanswers.com/hundredth-place-in-decimals). Therefore, the value of the digit in the hundreds place is 100 times greater than the value of the digit in the hundredths place.
Therefore, the answer is 100.
A scientist has two solutions, which she has labeled solution a and solution
b. each contains salt. she knows that solution a is 65% salt and solution b is 80% salt. she wants to obtain 150 ounces of a mixture that is 70% salt. how many ounces of each solution should she use?
2010 2008
$971 $812
$977 $943
$900 $873
$1071 $1023
$501 $486
2. What is the median weekly earnings of workers in the occupations listed for
2010?
The median weekly earnings of the data set of the workers in the occupations listed for 2010 is calculated as: $971.
How to Find the Median Weekly Earnings?To find the median weekly earnings for the occupations listed in 2010, we need to first arrange the earnings in order from least to greatest:
$501, $900, $971, $977, $1071
The median is the middle value in this ordered list. Since there are an odd number of values, the median is simply the middle value.
Therefore, the median weekly earnings of workers in the occupations listed for 2010 is $971.
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you are melting a rectangular block of wax to make candles. how many candles of the given shape can be made using a block that measures 10 cm by 9cm by 20 cm
The rectangular block of wax can make approximately 2 candles.
How do we determine the number of candles that could be made by that block of wax?To calculate the number of candles, we use the formula
V of wax = l x w x h = 10 cm x 9 cm x 20 cm = 1800 cubic cm
V of candle = l x w x h = 9 cm x 9 cm x 12 cm = 972 cubic cm
1800 / 972 = 1.85
The above answer is based on the full question below;
you are melting a rectangular block of wax to make candles. how many candles of the given shape can be made using a block that measures 10 cm by 9cm by 20 cm.
The height of the candle is 12cm and the base width is 9cm
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For the following exercises, convert the angle measures to degrees.
9π/5 b) - π/3
(round to two decimal places)
a) The measure of 9π/5 radians in degrees is approximately 324 degrees.
b) The measure of -π/3 radians in degrees is approximately -60 degrees.
To convert the given angle measures from radians to degrees, we can use the formula:
angle in degrees = (angle in radians) × (180/π)
a) To convert 9π/5 radians to degrees, we can substitute the given value in the above formula as:
angle in degrees = (9π/5) × (180/π) ≈ 324 degrees (rounded to two decimal places)
b) To convert -π/3 radians to degrees, we can substitute the given value in the above formula as:
angle in degrees = (-π/3) × (180/π) ≈ -60 degrees (rounded to two decimal places)
In general, we can convert an angle measure from radians to degrees by multiplying it by 180/π. Since π is an irrational number, the conversion factor 180/π is an irrational number as well. Therefore, when we round the result to two decimal places, we are actually approximating the true value of the angle measure.
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limit x->oo (sqrt(x^2-9x+1)-x)=?
I solved it up until -9x+1/((√x^2-9x+1)+x) but I don't know what to do after this.
Note that the limit of the expression as x approaches infinity is 1/2.
How did we arrive at this conclusion ?start by multiplying both the numerator and denominator by the conjugate expression
√ (x ² - 9x + 1) + x,
this will eliminates the root in the numerator
lim x->∞ [(√(x ² - 9x + 1) - x) * (√(x² - 9x + 1) + x)] / (√(x² - 9x + 1) + x)
Expanding the numerator
lim x- >∞ [(x² - 9x + 1) - x^2] / (√(x² - 9x + 1) + x)
Simplifying further:
lim x->∞ [(1 - 9/x + 1/ x²)] / (√(1 - 9/x + 1 /x²) + 1)
we can see that the 1/x ² term approaches zero, and the expression simplifies to
lim x->∞ [(1 - 0)] / (√(1 - 0) + 1)
= 1/2
So it is correct to state that the limit of the expression as x approaches infinity is 1/2.
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Use the substitution u = 1/y and v = 1/y to rewrite the equations in the system in terms of the variables u and v. Solve the system in terms of u and v. Then back substitute to determine the solution set to the original system in terms of x and y. -3/x + 4/y = 5 and 1/x - 2/y = -3
someone pls help i really need help with this
Answer:
50° F
Step-by-step explanation:
35 - -15= 50
Check
-15 + 50 = 35
And 35 - 50 = -15
Which shows one way to determine the factors of x³ + 5x² - 6x - 30 by grouping?
Ox(x²-5) + 6(x² - 5)
Ox(x²+5)-6(x²+ 5)
O x²(x - 5) + 6(x - 5)
O x²(x+5)-6(x+ 5)
Answer:
x^2(x+5)-6(x+5)!!!!!!!!
Find the missing information for both parts below.
The unknown angles in the circle are as follows:
a. m∠AEB = 73°
b. arc angle VW = 155°
How to find arc angles in a circle?a.
If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.
Therefore,
m∠AEB = 1 / 2 (99 + 47)
m∠AEB = 146 / 2
m∠AEB = 73 degrees
b.
If two secants intersect outside a circle , then the measure of an angle formed by the two lines is one half the positive difference of the measures of the intercepted arcs .
Therefore,'
arc angle VW = x
55 = 1 / 2 (x - 45)
55 = 0.5x - 22.5
0.5x = 55 + 22.5
0.5x = 77.5
divide both sides by 0.5
x = 77.5 / 0.5
x = 155 degrees
Therefore,
arc angle VW = 155 degrees
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Write two numbers that multiply to the value on top and add to the value on bottom.
8
8
−
6
−6
×
×
+
+
combine like terms 6x^2 - 10x + 21x - 35 = 6x^2 + 11x - 35
Answer:
Step-by-step explanation:
6x² - 10x + 21x - 35 = 6x² + 11x - 35
6x² - 6x² + 11x - 11x - 35 + 35 = 0
0 = 0
The equation is an identity. Its solution set is {all real numbers}.
The bells obtain a 30-year, $90,000 conventional mortgage at a 10.0% rate on a house selling for $120,000. Their monthly mortgage payment, including principal and interest, is $783.00. They also pay 2 points at closing.
A)What is total amount the Bells will pay for their house.
B) How much of the cost will be interest (including the 2 points)?
C) How much of the first payment on the mortgage is applied to the principal?
The total amount that the Bells will pay for their house would be $313, 680.
The cost that would be interest is $193, 680
The amount of the first payment going to mortgages is $165. 24
How to find the total amount paid ?Find the down payment :
Down payment = House price - Mortgage amount = $120,000 - $90,000 = $30,000
Then the points paid at closing :
= $ 90,000 x 0. 02 = $1,800
Total amount paid = Total mortgage payments + Down payment + Points cost
= 281, 880 + 30, 000 + 1, 800
= $ 313, 680
The total that is interest is:
Total interest paid = Total interest paid through monthly payments + Points cost
Total interest paid = $ 191, 880 + $ 1, 800 = $193, 680
The amount of the first payment going to principal is:
Principal portion of first payment = 90, 000 - 89, 834.76 = $165. 24
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Carson is organizing textbooks on his bookshelf. He has a Spanish textbook, a math textbook, a history textbook, and a health textbook. How many different ways can he line the textbooks up on his bookshelf?
Carson can line up his textbooks on his bookshelf in 24 different ways
What is Permutation?
Permutations are a way to count the number of ways that a set of objects can be arranged in a particular order. A permutation is an ordered arrangement of objects.
What is Combination?
The combination is a way to count the number of ways that a set of objects can be selected without regard to order. A combination is an unordered selection of objects.
According to the given information:
Carson has four textbooks that he wants to line up on his bookshelf. The number of different ways that he can do this is given by the permutation formula:
n! / (n - r)!
where n is the total number of objects (in this case, 4 textbooks), and r is the number of objects that he wants to arrange in a particular order (in this case, all 4 textbooks).
On substituting the values in the formula,
4! / (4 - 4)! = 4! / 0! = 4 x 3 x 2 x 1 / 1 = 24
Therefore, Carson can line up his textbooks on his bookshelf in 24 different ways.
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Can someone help me with this please
The matrix after the row operation is given as follows:
[tex]\left[\begin{array}{ccc}1&-\frac{4}{7}&\frac{8}{7}\\-12&7&-13\end{array}\right][/tex]
How to do the row operation?The matrix in the context of this problem is defined as follows:
[tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex]
We want to have element 1 into row 1 and column 1, that is, the element of 7 must assume a value of -1.
A valid row operation is the multiplication of the row by a constant, and as the element has a value of 7, the constant to obtain a value of 1 is:
7/k = 1
k = 7.
Dividing every element of the first row by 7, the matrix is given as follows:
[tex]\left[\begin{array}{ccc}1&-\frac{4}{7}&\frac{8}{7}\\-12&7&-13\end{array}\right][/tex]
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Which function does the dotted line represent explain how do you know
Answer:
Step-by-step explanation:
An inequality can be represented graphically as a region on one side of a line. Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region.
The space available for a relay race at a carnival is 92.75 yards. A rules sign is placed 5 yards before the starting line. If there are 5 sections of th
start to finish and each section covers the same distance, how long is each section of the race?
Each section of the race is (blank) yards long
If the total distance available is 92.75 yards, and there is a sign 5 yards before the starting line, the actual distance available for the race is:
92.75 - 5 = 87.75 yards
Since there are 5 sections of the race, each section covers:
87.75 / 5 = 17.55 yards
Therefore, each section of the race is 17.55 yards long.
For her geography project, Karen built a clay model of a
volcano in the shape of a cone. Her model has a diameter
of 12 inches and a height of 8 inches. Find the volume of
clay in her model to the nearest tenth. Use 3.14 for pi
Answer:
301.4 in^3
Step-by-step explanation:
Divide 12 by 2 to get the radius
12/2=6
Square 6 and multiply by 3.14 according to the area of a circle formula πr^2.
6^2=36 36*3.14=113.04
We now have the area of the base.
Multiply it by the height and divide by three to follow the formula for the volume of a cone, 1/3bh.
113.04*8=904.32. 904.32/3= 301.44, or 301.4 after rounding.
Solve for x. Round to the nearest tenth, if necessary
Using the tangent ratio, the value of x in the right triangle shown is calculated to the nearest tenth as: 2.6 units.
How to Find the Value of x Using the Tangent Ratio?The tangent ratio is part of the trigonometry ratios that is applied when solving a right triangle, and it is expressed as:
tan ∅ = length of the opposite side / length of the adjacent side.
We are given the following information from the image above:
Reference angle (∅) = 43 degrees
length of the opposite side = x
length of the adjacent side = 2.8
Plug in the values:
tan 43 = x/2.8
2.8 * tan 43 = x
x = 2.6 [to the nearest tenth]
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Can you help me rewrite this in other words?
Part a
H0: there is no association between climate change and certainty.
H1: there is no association between climate change and certainty.
2. The chi square equals 1947 with one degree of freedom and the p-value being a non-zero number.
3. Since the p-value is less than the significance level, which would be .05, we rejected null hypothesis that would show that there is a significant association between climate change and a certainty.
Part 2
H0: there is no association between sleeping and the income class.
H1: there is a association between the income class and sleeping.
2. The chi square was 119.864 with 12 different degrees of freedom the p value for this is also a non-zero number.
3. Since the p value is less than .05, we would reject to null hypothesis, which would make sense that there is a significant association between sleeping and income class.
The discussion for both cases is shown below.
Part a:
H0: there is no association between climate change and certainty.
H1: there is no association between climate change and certainty.
It seems that the null hypothesis (H0) and the alternative hypothesis (H1) are identical, which doesn't make sense. Typically, the null hypothesis states that there is no association or effect, while the alternative hypothesis states that there is an association or effect.
The statement also mentions that the p-value is a non-zero number, but it doesn't provide the actual value. The p-value is used to determine the statistical significance of the association and should be compared to a predetermined significance level (e.g., 0.05) to make a decision.
Part 2:
H0: there is no association between sleeping and the income class.
H1: there is a association between the income class and sleeping.
Similarly, the null hypothesis (H0) and the alternative hypothesis (H1) are stated incorrectly. The null hypothesis should state no association or effect, while the alternative hypothesis should state that there is an association or effect.
Again, the statement mentions a non-zero p-value but doesn't provide the actual value. The p-value needs to be compared to a significance level to determine the statistical significance of the association.
In both cases, it is important to provide the actual p-value and compare it to the significance level to make a proper conclusion about the association between the variables.
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Question 2 (2 points)
In the circle below, D is the center and segment AC is the diameter.
What is the measure of ZADC?Blank 1:
Blank 2
What is the measure of ZABC?
The measure of ∠ADC is equal to 180 degrees.
The measure of ∠ABC is equal to 90 degrees.
What is a circle?In Mathematics and Geometry, a circle simply refers to a closed, two-dimensional (2D) curved geometric shape with no edges or corners. Additionally, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).
Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can reasonably infer and logically deduce that the measure of angle ADC (∠ADC) is equal to 180 degrees.
In conclusion, the angle subtended by chord AB at point B has a measure of 90 degrees.
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What are some common order of operation mistakes that students make when evaluating expressions? Make a list and share two examples in the Discussion Board; then explore the lists your peers have posted and respond to one that you find particularly insightful.
Some of the common order of operation mistakes that students make when evaluating expressions are the use of basic mathematical operations.
What is a mistake?You should know that an error or fault results from defective judgment, deficient knowledge, or carelessness.
A combination of numbers, letters, and relational operators containing at least one operation is deemed a mathematical expression. Additionally, it must also include variables and/or numbers, excluding an equal sign.
Some prevalent errors include using both a positive and a negative sign, using two negative signs, and misusing brackets.
By being unable to comprehend the problems accurately, learners often commit significant errors while assessing formulations, which underscores the importance of employing fundamental mathematical operations.
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I need help with this please.
1/2 x 3 x 3 = 4.5
I just need help on how 4.5 is the answer.
Answer:
3
Step-by-step explanation:
3 * 3 = 6
1/2 * 6 = 3 not 4.5
Because, when we multiply with 1/2, we are actually dividing the number by 2, and 6/2 = 3.
The 3 x 3 part turns into 9
So we have 1/2 x 9 or 9/2
Use long division to find that 9/2 gives a quotient of 4 and remainder 1
Imagine you had 9 cookies and 2 friends. Each friend would get 4 cookies each, eating 4*2 = 8 cookies overall. Then there's 9-8 = 1 cookie as the remainder.
The "remainder 1" then leads to 1/2 = 0.5
quotient = 4
remainder = 1 ---> decimal portion = 1/2 = 0.5
So that's how we get to 4+0.5 = 4.5
You can use a calculator to see that 9/2 = 4.5
Category: nr percentages
question_id: 5782
Alex is really upset. He invested a lot of money in shares and only has $72,800 left of his original
investment. His shares dropped in value by 35% in 4 days. What amount did Alex pay for his shares
to being with?
Answer:
Let's start by using algebra to solve for the original amount that Alex paid for his shares.
Let X be the original amount that Alex paid for his shares.
We know that his shares dropped in value by 35%, so after the drop, he had 65% of his original investment left:
0.65X = $72,800
Solving for X:
X = $72,800 / 0.65
X = $112,000
Therefore, Alex paid $112,000 for his shares to begin with.